B0375
Title: Convergence guarantees for response prediction in latent structure networks on unknown one-dimensional manifolds
Authors: Aranyak Acharyya - Johns Hopkins University (United States) [presenting]
Joshua Agterberg - University of Pennsylvania (United States)
Michael Trosset - Indiana University Bloomington (United States)
Youngser Park - Johns Hopkins University (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: In recent times the popularity of random graphs has increased in different domains of science owing to their applicability in modelling networks. Random dot product graphs form a particular category of random graphs where each node is associated with a typically unobserved vector known as the latent position vector, and the probability of the formation of an edge between a pair of nodes is given by the inner product of the corresponding latent position vectors. The model involves a random dot product graph whose latent positions lie on an unknown one-dimensional manifold in a high-dimensional ambient space, and some nodes are coupled with a response covariate. A technique is proposed that exploits the presence of the auxiliary nodes to capture the underlying manifold structure and predicts the response at unlabeled nodes under certain model assumptions. Convergence guarantees are established for the technique and demonstrate its performance on synthetic data.
